3D mapping vs localization accuracy of tvec

[messileonardo]

I would like to ask whoever can help me clarification about 3D mapping and localization accuracy of tvec. I did this experiment:

1. I choose 20 positions in a grid in which each point is 1 meter distant each other. I assumed the first position in the bottom left side is (0,0,0). From this assumption I have the real position of each photo.
2. For each position, I shot 2 photos using a camera stand.
3. I used 1 photo for each position for the 3d mapping (green frustum below) and then I localized the remaining ones (red frustum below).
4. 3d mapping ("sfm") and localization ("loc") parameters
5. I scaled the sfm model using the model_aligner function in colmap giving the real position of 3 photos.
6. I computed the average errors (measured as linear distance and using ransac.max_error = 12) between

• tvec error between mapping (green frustum) and localization (red frustum) photos: 0.060 m

• tvec error between mapping (green frustum) and real positions: 0.030 m

• tvec error between localization (red frustum) and real positions: 0.067 m

  7. I replicated the same experiment using as ransac.max_error = 4 and I computed the average errors (measured as linear distance) between

• tvec error between mapping (green frustum) and localization (red frustum) photos: 0.169 m

• tvec error between mapping (green frustum) and real positions: 0.030 m

• tvec error between localization (red frustum) and real positions: 0.174 m

and finally using as ransac.max_error = 50 and I computed the average errors (measured as linear distance) between

• tvec error between mapping (green frustum) and localization (red frustum) photos: 0.096 m
• tvec error between mapping (green frustum) and real positions: 0.029 m
• tvec error between localization (red frustum) and real positions: 0.101 m
  8. My questions are
• Why 3d mapping is more accurate than localization? I am aware that configuration parameters are different between 3d mapping and localization (I did that to make localization faster), but this can be the real explanation?
• Why tvec error are higher with ransac.max_error = 4 than with ransac.max_error = 12 or 50? What is the real meaning of the ransac.max_error and what is the logic for a proper setting?

Many thanks in advance to everyone can help me!

[messileonardo]

With reference to the first question " Why 3d mapping is more accurate than localization? I am aware that configuration parameters are different between 3d mapping and localization (I did that to make localization faster), but this can be the real explanation? " I did another test with the same configuration between 3d mapping and localization and I copmuted the average errors (measured as linear distance and using ransac.max_error = 12) between

• tvec error between mapping (green frustum) and localization (red frustum) photos: 0.064 m
• tvec error between mapping (green frustum) and real positions: 0.028 m
• tvec error between localization (red frustum) and real positions: 0.074 m

Error are very similar to the case with different configuration. So, why 3d mapping is more accurate than localization (about 3 cm error vs 6.5 cm error respectively)? Many thanks

[messileonardo]

I will try to sum up my questions.

1. What could be possible causes of different accuracy between mapping (about 3 cm error) and localization (about 6.5 cm error)?
2. Since I noticed that lower ransac.max_error threshold do not provide better localization results, what could be the logic to follow to properly set this value?

Many thanks to everyone can help me.

[sarlinpe]

The mapping of each image starts the estimate the absolute pose, which is identical to the localization process, and it followed by a retriangulation of the 3D points and by a full bundle adjustment, which refines both poses and camera intrinsic parameters. This explains why mapping poses and more accurate than poses estimated by the localization process.

[messileonardo]

Many thanks @sarlinpe ! What about ransac.max_error threshold during localization? Can you suggest a logic to set it or a minimum number of inliers to get for a good localization or what else? Thanks again!

[sarlinpe]

It depends on your data. The default value is generally sufficient, and it can be decreased if necessary.